# Video Lectures

### Sums of certain arithmetic functions over 𝔽q[T] and non-unitary distributions

In 2018 Keating, Rodgers, Roditty-Gershon and Rudnick established relationships of the mean-square of sums of the divisor function $d_k(f)$ over short intervals and over arithmetic progressions for the function field $\mathbb{F}_q[T]$ to certain...

### The Ruelle invariant and convexity in higher dimensions

I will explain how to construct the Ruelle invariant of a symplectic cocycle over an arbitrary measure preserving flow. I will provide examples and computations in the case of Hamiltonian flows and Reeb flows (in particular, for toric domains). As...

### Gaussian multiplicative chaos: applications and recent developments

Nina Holden

I will give an introduction to Gaussian multiplicative chaos and some of its applications, e.g. in Liouville theory. Connections to random matrix theory and number theory will also be briefly discussed.

### Number theoretic aspects of multiplicative chaos

Multiplicative chaos is the general name for a family of probabilistic objects, which can be thought of as the random measures obtained by taking the exponential of correlated Gaussian random variables. Multiplicative chaos turns out to be closely...

### Large sieve inequalities for families of L-functions

Matt Young

Large sieve inequalities are useful and flexible tools for understanding families of L-functions.  The quality of the bound is one measure of our understanding of the corresponding family.  For instance, they may directly give rise to good bounds...

### The distribution of values of zeta and L-functions

I will survey recent progress on understanding the value distribution of zeta and L-functions.  In particular I will discuss the problem of moments of the zeta function on the critical line, and central  values of L-functions, where the last twenty...

### Opening Remarks and History of the math talks

Peter Sarnak, Jon Keating and Hugh Montgomery

On April 6, 1972 a young graduate student named Hugh Montgomery and the world-renowned mathematical physicist Freeman Dyson had a conversation in the tearoom at the Institute for Advanced Study which led to a fusion of two disparate fields and an...

### Opening Remarks and History of the math talks

Peter Sarnak, Jon Keating and Hugh Montgomery

On April 6, 1972 a young graduate student named Hugh Montgomery and the world-renowned mathematical physicist Freeman Dyson had a conversation in the tearoom at the Institute for Advanced Study which led to a fusion of two disparate fields and an...

### Locality and deformations in relative symplectic cohomology

Yoel Groman

Relative symplectic cohomology is a Floer theoretic invariant associated with compact subsets K of a closed or geometrically bounded symplectic manifold M. The motivation for studying it is that it is often possible to reduce the study of global...